1. Field of the Invention
This invention relates generally to density measuring devices and more specifically to a method and apparatus for measuring density of a flowing compressible gas on a real time basis.
2. State of the Prior Art
There are many reasons for measuring density of a flowing compressible gas. One example is in dispensing and measuring compressed natural gas (CNG) into a customer's vehicle tank at the point of sale. As explained in U.S. Pat. No. 5,238,030, which is incorporated herein by reference, mass flow rate m of natural gas can be measured quite accurately with a mass flow meter comprising a sonic nozzle. At a given gas temperature and pressure at the entrance of a sonic nozzle, i.e., a nozzle in which flow is choked, the mass flow rate m of the gas flowing through the nozzle remains constant regardless of variations in pressure downstream of the nozzle. Therefore, by knowing some information about the specific sonic nozzle being used, including the nozzle discharge coefficient Cd and the cross-sectional area of the nozzle throat A.sub.t, by measuring stagnant pressure P.sub.o and temperature T.sub.o of the gas immediately upstream of the sonic nozzle, and knowing the specific heat ratio k and the universal gas constant R of the gas, the mass flow rate m of the gas flowing through the nozzle can be determined according to the relationship: ##EQU1##
However, natural gas does not always have the same molecular composition, thus also does not always have the same specific heat ratio k, which can vary. Consequently, mass flow rate m determinations according to the relationship above is not always accurate, if the specific heat ratio k is presumed to be constant when it really varies.
The modified sonic nozzle flow dispenser for compressed natural gas (CNG) described in U.S. Pat. No. 5,564,306, issued Oct. 15, 1996 which is also incorporated herein by reference, provides a method and apparatus for determining specific heat ratio k of the natural gas on a real time basis as the natural gas flows through the sonic nozzle. In that invention, the specific heat ratio k is determined as a function of the ratio of a gas pressure P.sub.i inside the nozzle to the gas pressure P.sub.o immediately upstream of the nozzle. Mass flow rate m can then be determined by measuring the density .rho..sub.o of the natural gas at the stagnant pressure P.sub.o immediately upstream of the sonic nozzle and then calculating the mass flow rate m as a function of the density .rho..sub.o, the pressure ratio (P.sub.i /P.sub.o), and the specific heat ratio k.
There are a number of good densitometers that can be used to determine the density .rho..sub.o of the natural gas for the purpose of calculating mass flow rate m in CNG dispensers as described above or for any number of other purposes. However, such state-of-the-art densitometers that can produce accurate enough density measurements on a real time basis for use in accurate measurements of mass flow rate m in natural gas dispensers where customers are charged for the natural gas according to such measurements tend to be very expensive and difficult to install in a manner that measures gas density .rho..sub.o at the stagnant pressure P.sub.o immediately upstream of the sonic nozzle. Space requirements, noise and pressure fluctuations, and sensitive densitometer components make it difficult and expensive to obtain accurate gas density .rho..sub.o measurements in these circumstances.